Abstract
The purpose of this research was to discuss the un-differentiable features hidden in observed earthquake acceleration records. On the assumption that the Fourier transformations of acceleration time history, such as the real and imaginary parts as well as the amplitude and phase, are continuous stochastic process with respect to (wrt) the circular frequency, we investigated their stochastic characteristics such as the mean square sum and the distribution feature. We found that probability distribution functions of the first derivative of real and imaginary parts of the Fourier transform of acceleration time history wrt the circular frequency were expressed by the Levy flight distribution with same parameters. This resulted in that the real and imaginary parts were un-differentiable function wrt the circular frequency because the variance of Levy flight distribution could not be defined. Based on this fact we, therefore, suggested a possibility that the jerk (the derivation of acceleration wrt time) of observed acceleration records is a discontinuous functions wrt time.
